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Ratio tests for the convergence of integrals

Published online by Cambridge University Press:  31 October 2008

W. L. Ferrar
W. L. Ferrar
Affiliation:
Hertford College, Oxford.
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1. Ratio tests for the convergence or divergence of infinite series of positive terms are well known; they are used in and out of season. On the other hand, ratio tests for infinite integrals are never used. What is the reason for this disparity between series and integrals?

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 31 , January 1939 , pp. i - iii
Copyright
Copyright © Edinburgh Mathematical Society 1939

References

1 We need some condition to ensure that f(x) φ(x) is the integral of its differential coefficient; we have chosen the simplest.